anova.cca {vegan} | R Documentation |
The function performs an ANOVA like permutation test for Constrained
Correspondence Analysis (cca
), Redundancy Analysis
(rda
) or Constrained Analysis of Principal Coordinates
(capscale
) to assess the significance of constraints.
## S3 method for class 'cca': anova(object, alpha=0.05, beta=0.01, step=100, perm.max=9999, by = NULL, ...) permutest(x, ...) ## S3 method for class 'cca': permutest(x, permutations = 100, model = c("reduced", "direct", "full"), first = FALSE, strata, ...)
object,x |
A result object from cca . |
alpha |
Targeted Type I error rate. |
beta |
Accepted Type II error rate. |
step |
Number of permutations during one step. |
perm.max |
Maximum number of permutations. |
by |
Setting by = "axis" will assess significance for each
constrained axis, and setting by = "terms" will assess
significance for each term (sequentially from first to last), and
setting by = "margin" will assess the marginal effects of the
terms (each marginal term analysed in a model with all other
variables). |
... |
Parameters passed to other functions.
anova.cca passes all arguments to
permutest.cca . In anova with by = "axis" you
can use argument cutoff (defaults 1 ) which stops
permutations after exceeding the given level. |
permutations |
Number of permutations for assessing significance of constraints. |
model |
Permutation model (partial match). |
first |
Assess only the significance of the first constrained
eigenvalue; will be passed from anova.cca . |
strata |
An integer vector or factor specifying the strata for permutation. If supplied, observations are permuted only within the specified strata. |
Functions anova.cca
and permutest.cca
implement an ANOVA
like permutation test for the joint effect of constraints in
cca
, rda
or capscale
.
Functions anova.cca
and permutest.cca
differ in printout
style and in interface.
Function permutest.cca
is the proper workhorse, but
anova.cca
passes all parameters to permutest.cca
.
In anova.cca
the number of permutations is controlled by
targeted “critical” P value (alpha
) and accepted Type
II or rejection error (beta
). If the results of permutations
differ from the targeted alpha
at risk level given by
beta
, the permutations are
terminated. If the current estimate of P does not
differ significantly from alpha
of the alternative hypothesis,
the permutations are
continued with step
new permutations (at the first step, the
number of permuations is step - 1
). However, with by =
"terms"
a fixed number of permutations will be used, and this
is given by argument permutations
, or if this is missing,
by step
.
The function permutest.cca
implements a permutation test for
the “significance” of constraints in cca
,
rda
or capscale
. Community data are
permuted with choice model = "direct"
, residuals after
partial CCA/RDA/CAP with choice model = "reduced"
(default),
and residuals after CCA/RDA/CAP under choice model = "full"
.
If there is no partial CCA/RDA/CAP stage, model = "reduced"
simply permutes the data and is equivalent to model = "direct"
.
The test statistic is ``pseudo-F'',
which is the ratio of constrained and unconstrained total Inertia
(Chi-squares, variances or something similar), each divided by their
respective ranks. If there are no conditions (“partial” terms), the
sum of all eigenvalues remains constant, so that pseudo-F and
eigenvalues would give equal results. In partial CCA/RDA/CAP, the
effect of conditioning variables (“covariables” is removed before
permutation, and these residuals are added to the non-permuted fitted
values of partial CCA (fitted values of X ~ Z
). Consequently,
the total Chi-square is not fixed, and test based on pseudo-F
would differ from the test based on plain eigenvalues. CCA is a
weighted method, and environmental data are re-weighted at each
permutation step using permuted weights.
The default test is for the sum of all constrained eigenvalues.
Setting first = TRUE
will perform a test for the first
constrained eigenvalue. Argument first
can be set either in
anova.cca
or in permutest.cca
. It is also possible to
perform significance tests for each axis or for each term
(constraining variable) using argument by
in
anova.cca
. Setting by = "axis"
will perform separate
significance tests for each constrained axis. All previous
constrained axes will be used as conditions (“partialled
out”) and a test for the first constrained eigenvalues is
performed. You can stop permutation tests after exceeding a given
signficance level with argument cutoff
to speed up
calculations in large models. Setting by = "terms"
will
perform separate significance test for each term (constraining
variable). The terms are assessed sequentially from first to last,
and the order of the terms will influence their
significances. Setting by = "margin"
will perform separate
significance test for each marginal term in a model with all other
terms. The marginal test also accepts a scope
argument for
the drop.scope
which can be a character vector of term
labels that are analysed, or a fitted model of lower scope. The
marginal effects are also known as “Type III” effects, but
the current function only evaluates marginal terms. It will, for
instance, ignore main effects that are included in interaction
terms. In calculating pseudo-F, all terms are compared to the
same residual of the full model. Permutations for all axes or terms
will start from the same .Random.seed
, and the seed
will be advanced to the value after the longest permutation at the
exit from the function.
Function permutest.cca
returns an object of class
"permutest.cca"
, which has its own print
method. The
function anova.cca
calls permutest.cca
, fills an
anova
table and uses print.anova
for printing.
The default permutation model
changed from "direct"
to
"reduced"
in vegan version 1.14-11 (release version
1.15-0), and you must explicitly set model = "direct"
for
compatibility with the old version.
Tests by = "terms"
and by = "margin"
are consistent
only when model = "direct"
.
Jari Oksanen
Legendre, P. and Legendre, L. (1998). Numerical Ecology. 2nd English ed. Elsevier.
cca
, rda
, capscale
to get something to analyse. Function drop1.cca
calls
anova.cca
with by = "margin"
, and
add1.cca
an analysis for single terms additions, which
can be used in automatic or semiautomatic model building (see
deviance.cca
).
data(varespec) data(varechem) vare.cca <- cca(varespec ~ Al + P + K, varechem) ## overall test anova(vare.cca) ## Test for axes anova(vare.cca, by="axis", perm.max=500) ## Sequential test for terms anova(vare.cca, by="terms", permu=200) ## Marginal or Type III effects anova(vare.cca, by="margin") ## Marginal test knows 'scope' anova(vare.cca, by = "m", scope="P")